Question 7 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2017
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Find \(\int ( 2 \cos \theta - 3 ) ( \cos \theta + 1 ) \mathrm { d } \theta\).
1. Find \(\int \left( \frac { 4 } { 2 x + 1 } + \frac { 1 } { 2 x } \right) \mathrm { d } x\).
2. Hence find \(\int _ { 1 } ^ { 4 } \left( \frac { 4 } { 2 x + 1 } + \frac { 1 } { 2 x } \right) \mathrm { d } x\), giving your answer in the form \(\ln k\).